The use of spectral techniques for the computation of the expected power output of linear time invariant filters subjected to a nonstationary noise is studied. The two-dimensional power spectrum is defined, and its use for computing the time varying expected power output is illustrated. The derivation of the one-dimensional energy spectrum from the two-dimensional power spectrum is shown. The derivation of the instantaneous power spectrum as the derivative of the truncated energy spectrum is shown. It is concluded that the instantaneous power spectrum is not a useful engineering technique since there are no expressions relating the instantaneous power spectrum at the filter output to that at the input. For the special case in which the nonstationary noise is the product of a modulation function and a stationary noise, it is shown that the problem can often be reduced to an eguivalent stationary problem and solved in a well known way. (Author).
Mathematical properties are defined and developed for three different types of spectra which can be associated with nonstationary random process: double frequency spectra, time varying spectra, and time averaged spectra. The double frequency spectra is the double Fourier transform of the nonstationary covariance function and indicates the correlation between frequencies. The time varying spectra, based upon narrow band filtering and ensemble averaging, indicates relations between frequency and time. The time averaged spectra is obtained by taking a time average of the time varying spectra. A significant measurement problem exists for the first two representations because they are two-dimensional functions, whereas the third representation is directly measurable. However, the third procedure is restricted in its applications, while the first two are suitable for general problems. Each of these spectra is computed for a particular nonstationary example, and some experimental results are shown to verify the theory. (Author).
The purpose of the workshop was to bring together researchers working in a broad spectrum of nonstationary stochastic processes to present their findings and techniques for analyzing the growing field of nonstationary stochastic processes. Researchers from both engineering and mathematics communities shared their sometimes different, but complementing, point of views on the recent developments in the theory and applications of nonstationary stochastic processes. As such, this volume will be of interest to mathematicians, probabilists, and engineers, and it is hoped that this will stimulate a significant amount of research in this field.
Nonstationarity is another name for intermittency, a phenomenon which affects many physical processes. Data collected in many R&D programs frequently exhibit nonstationary features, and problems inherent in the analysis of such data are profound. The premier objective of these proceedings is to consolidate recent developments in nonstationary analysis. A second objective is to delineate open problems. A by-product will hopefully be a bridging of the gap between related governmental needs, and the present-day research capabilities of both academics and non-academics alike.
This book covers the basic topics associated with the measurement, analysis and simulation of random environmental processes which are encountered in practice when dealing with the dynamics, fatigue and reliability of structures in real environmental conditions. The treatment is self-contained and the authors have brought together and integrated the most important information relevant to this topic in order that the newcomer can see and study it as a whole. This approach should also be of interest to experienced engineers from fatigue laboratories who want to learn more about the possible methods of simulation, especially for use in real time on electrohydraulic computer-controlled loading machines.Problems of constructing a measuring system are dealt with in the first chapter. Here the authors discuss the choice of measuring conditions and locations, as well as the organization of a chain of devices for measuring and recording random environmental processes. Some experience gained from practical measurements is also presented. The recorded processes are further analysed by various methods. The choice is governed by the aims of the measurements and applications of the results. Chapter 2 is thus devoted to methods of random process evaluations for digital computers, both from the fatigue and dynamic point of view. The most important chapter is Chapter 3 as this presents a review of up-to-date methods of random process simulation with given statistical characteristics. These methods naturally follow those of random process analysis, and their results form initial data for the corresponding simulations algorithms, including occurrences of characteristic parameters of counting methods, reproduction of correlation theory characteristics and of autoregressive models. The simulation of non-stationary processes is treated in depth, taking into account their importance for practical applications and also the lack of information of this subject.The book is intended to help resolve many practical problems concerning the methods and quality of environmental process evaluation and simulation which can arise when up-to-date loading systems with computer control are being used in material, component and structural fatigue and dynamic research.
The use of standard techniques for measuring the power spectra of stationary phenomena in the treatment of nonstationary physical phenomena can lead to erroneous results. Some of the tools available for the analysis of nonstationary random phenomena are outlined in this report and the applicability of these tools to some practical engineering problems is discussed.
